Semantic Spaces Dissertation

Title: Semantic Spaces

Authors:Yuri Manin, Matilde Marcolli

(Submitted on 13 May 2016)

Abstract: Any natural language can be considered as a tool for producing large databases (consisting of texts, written, or discursive). This tool for its description in turn requires other large databases (dictionaries, grammars etc.). Nowadays, the notion of database is associated with computer processing and computer memory. However, a natural language resides also in human brains and functions in human communication, from interpersonal to intergenerational one. We discuss in this survey/research paper mathematical, in particular geometric, constructions, which help to bridge these two worlds. In particular, in this paper we consider the Vector Space Model of semantics based on frequency matrices, as used in Natural Language Processing. We investigate underlying geometries, formulated in terms of Grassmannians, projective spaces, and flag varieties. We formulate the relation between vector space models and semantic spaces based on semic axes in terms of projectability of subvarieties in Grassmannians and projective spaces. We interpret Latent Semantics as a geometric flow on Grassmannians. We also discuss how to formulate G\"ardenfors' notion of "meeting of minds" in our geometric setting.

Submission history

From: Matilde Marcolli [view email]
[v1] Fri, 13 May 2016 16:25:38 GMT (112kb)

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

Но это же абсурд, - не согласилась Сьюзан.  - Ни один из новых шифрованных файлов нельзя вскрыть без «ТРАНСТЕКСТА». Вероятно, «Цифровая крепость» - это стандартный алгоритм для общего пользования, тем не менее эти компании не смогут его вскрыть. - Это блистательная рекламная операция, - сказал Стратмор.  - Только подумай - все виды пуленепробиваемого стекла непроницаемы для пуль, но если компания предлагает вам попробовать пробить ее стекло, все хотят это сделать.

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